Obstructions could be inward opening windows or fly screens, which may not be accessible if you inside mount your shutter. Other obstructions, such as window winders, handles, locks, keys, alarm boxes are fine - as long as you have enough clearance between the end of your obstruction to the end of the recess.
Even with a deep recess, your window may have obstructions that could get in the way of inside mounting your shutters; but there are ways around this!
HOW MUCH CLEARANCE DO I NEED FOR AN INSIDE MOUNT?
As a general rule, 70mm of clearance is required from the furthest point on your window to the edge of the recess for inside mounting. This is so that the shutter blades can be opened completely without hitting the window pane. However, this requirement is relatively conservative and the exact clearance needed ultimately depends on the type of frame you will be using.
HOW DO I GET AROUND AN OBSTRUCTION?
To begin with, it's important to differentiate between the shutter panels and the frame itself. The frame will create a border around the inside of your window recess, while the shutters will hinge inside the frame.